Question

given the function defined in the table be change, in simplest form, of the function ov

$x$	$f(x)$
2	73
3	66
4	59
5	52

Explanation:

Step1: Identify the type of function

We have a table of values for \( x \) and \( f(x) \). Let's check the differences between consecutive \( f(x) \) values.
For \( x = 1 \) to \( x = 2 \): \( 73 - 80 = -7 \)
For \( x = 2 \) to \( x = 3 \): \( 66 - 73 = -7 \)
For \( x = 3 \) to \( x = 4 \): \( 59 - 66 = -7 \)
For \( x = 4 \) to \( x = 5 \): \( 52 - 59 = -7 \)
The common difference is \( -7 \), so this is a linear function with slope (rate of change) \( m=-7 \).

Step2: Find the rate of change

The rate of change (slope) of a linear function is given by \( \frac{\Delta f(x)}{\Delta x} \). Since \( \Delta x = 1 \) (consecutive \( x \)-values) and \( \Delta f(x) = -7 \) (as calculated above), the rate of change is \( -7 \).

Answer:

\( -7 \)